{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When we talk about quantum computing, we actually talk about several different paradigms. The most common one is gate-model quantum computing, in the vein we discussed in the previous notebook. In this case, gates are applied on qubit registers to perform arbitrary transformations of quantum states made up of qubits.\n",
    "\n",
    "The second most common paradigm is quantum annealing. This paradigm is often also referred to as adiabatic quantum computing, although there are subtle differences. Quantum annealing solves a more specific problem -- universality is not a requirement -- which makes it an easier, albeit still difficult engineering challenge to scale it up. The technology is up to 2000 superconducting qubits in 2018, compared to the less than 100 qubits on gate-model quantum computers. D-Wave Systems has been building superconducting quantum annealers for over a decade and this company holds the record for the number of qubits -- 2048. More recently, an IARPA project was launched to build novel superconducting quantum annealers. A quantum optics implementation was also made available by QNNcloud that implements a coherent Ising model. Its restrictions are different from superconducting architectures.\n",
    "\n",
    "Gate-model quantum computing is conceptually easier to understand: it is the generalization of digital computing. Instead of deterministic logical operations of bit strings, we have deterministic transformations of (quantum) probability distributions over bit strings. Quantum annealing requires some understanding of physics, which is why we introduced classical and quantum many-body physics in a previous notebook. Over the last few years, quantum annealing inspired gate-model algorithms that work on current and near-term quantum computers (see the notebook on variational circuits). So in this sense, it is worth developing an understanding of the underlying physics model and how quantum annealing works, even if you are only interested in gate-model quantum computing.\n",
    "\n",
    "While there is a plethora of quantum computing languages, frameworks, and libraries for the gate-model, quantum annealing is less well-established. D-Wave Systems offers an open source suite called Ocean. A vendor-independent solution is XACC, an extensible compilation framework for hybrid quantum-classical computing architectures, but the only quantum annealer it maps to is that of D-Wave Systems. Since XACC is a much larger initiative that extends beyond annealing, we choose a few much simpler packages from Ocean to illustrate the core concepts of this paradigm. However, before diving into the details of quantum annealing, it is worth taking a slight detour to connect the unitary evolution we discussed in a closed system and in the gate-model paradigm and the Hamiltonian describing a quantum many-body system. We also briefly discuss the adiabatic theorem, which provides the foundation why quantum annealing would work at all."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Unitary evolution and the Hamiltonian\n",
    "\n",
    "We introduced the Hamiltonian as an object describing the energy of a classical or quantum system. Something more is true: it gives a description of a system evolving with time. This formalism is expressed by the Schrödinger equation:\n",
    "\n",
    "$$\n",
    "\\imath\\hbar {\\frac {d}{dt}}|\\psi(t)\\rangle = H|\\psi(t)\\rangle,\n",
    "$$\n",
    "\n",
    "where $\\hbar$ is the reduced Planck constant. Previously we said that it is a unitary operator that evolves state. That is exactly what we get if we solve the Schrödinger equation for some time $t$: $U = \\exp(-\\imath Ht/\\hbar)$. Note that we used that the Hamiltonian does not depend on time. In other words, every unitary we talked about so far has some underlying Hamiltonian.\n",
    "\n",
    "The Schrödinger equation in the above form is the time-dependent variant: the state depends on time. The time-independent Schröndinger equation reflects what we said about the Hamiltonian describing the energy of the system:\n",
    "\n",
    " $$\n",
    " H|\\psi \\rangle =E|\\psi \\rangle,\n",
    "$$\n",
    "\n",
    "where $E$ is the total energy of the system."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The adiabatic theorem and adiabatic quantum computing\n",
    "\n",
    "An adiabatic process means that conditions change slowly enough for the system to adapt to the new configuration. For instance, in a quantum mechanical system, we can start from some Hamiltonian $H_0$ and slowly change it to some other Hamiltonian $H_1$. The simplest change could be a linear schedule:\n",
    "\n",
    "$$\n",
    "H(t) = (1-t) H_0 + t H_1,\n",
    "$$\n",
    "\n",
    "for $t\\in[0,1]$ on some time scale. This Hamiltonian depends on time, so solving the Schrödinger equation is considerably more complicated. The adiabatic theorem says that if the change in the time-dependent Hamiltonian occurs slowly, the resulting dynamics remain simple: starting close to an eigenstate, the system remains close to\n",
    "an eigenstate. This implies that if the system started in the ground state, if certain conditions are met, the system stays in the ground state. \n",
    "\n",
    "We call the energy difference between the ground state and the first excited state the gap. If $H(t)$ has a nonnegative gap for each $t$ during the transition and the change happens slowly, then the system stays in the ground state. If we denote the time-dependent gap by $\\Delta(t)$, a course approximation of the speed limit scales as $1/\\min(\\Delta(t))^2$.\n",
    "\n",
    "This theorem allows something highly unusual. We can reach the ground state of an easy-to-solve quantum many body system, and change the Hamiltonian to a system we are interested in. For instance, we could start with the Hamiltonian $\\sum_i \\sigma^X_i$ -- its ground state is just the equal superposition. Let's see this on two sites:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-11-19T20:07:55.833895Z",
     "start_time": "2018-11-19T20:07:55.714483Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eigenvalues: [-2. -0.  0.  2.]\n",
      "Eigenstate for lowest eigenvalue [-0.5 -0.5 -0.5 -0.5]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "np.set_printoptions(precision=3, suppress=True)\n",
    "\n",
    "X = np.array([[0, 1], [1, 0]])\n",
    "IX = np.kron(np.eye(2), X)\n",
    "XI = np.kron(X, np.eye(2))\n",
    "H_0 = - (IX + XI)\n",
    "λ, v = np.linalg.eigh(H_0)\n",
    "print(\"Eigenvalues:\", λ)\n",
    "print(\"Eigenstate for lowest eigenvalue\", v[:, 0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we could turn this Hamiltonian slowly into a classical Ising model and read out the global solution.\n",
    "\n",
    "<img src=\"figures/annealing_process.svg\" alt=\"Annealing process\" style=\"width: 400px;\"/>\n",
    "\n",
    "\n",
    "Adiabatic quantum computation exploits this phenomenon and it is able to perform universal calculations with the final Hamiltonian being $H=-\\sum_{<i,j>} J_{ij} \\sigma^Z_i \\sigma^Z_{j} - \\sum_i h_i \\sigma^Z_i - \\sum_{<i,j>} g_{ij} \\sigma^X_i\\sigma^X_j$. Note that is not the transverse-field Ising model: the last term is an X-X interaction. If a quantum computer respects the speed limit, guarantees the finite gap, and implements this Hamiltonian, then it is equivalent to the gate model with some overhead.\n",
    "\n",
    "The quadratic scaling on the gap does not appear too bad. So can we solve NP-hard problems faster with this paradigm? It is unlikely. The gap is highly dependent on the problem, and actually difficult problems tend to have an exponentially small gap. So our speed limit would be quadratic over the exponentially small gap, so the overall time required would be exponentially large."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Quantum annealing\n",
    "\n",
    "A theoretical obstacle to adiabatic quantum computing is that calculating the speed limit is clearly not trivial; in fact, it is harder than solving the original problem of finding the ground state of some Hamiltonian of interest. Engineering constraints also apply: the qubits decohere, the environment has finite temperature, and so on. *Quantum annealing* drops the strict requirements and instead of respecting speed limits, it repeats the transition (the annealing) over and over again. Having collected a number of samples, we pick the spin configuration with the lowest energy as our solution. There is no guarantee that this is the ground state.\n",
    "\n",
    "Quantum annealing has a slightly different software stack than gate-model quantum computers. Instead of a quantum circuit, the level of abstraction is the classical Ising model -- the problem we are interested in solving must be in this form. Then, just like superconducting gate-model quantum computers, superconducting quantum annealers also suffer from limited connectivity. In this case, it means that if our problem's connectivity does not match that of the hardware, we have to find a graph minor embedding. This will combine several physical qubits into a logical qubit. The workflow is summarized in the following diagram [[1](#1)]:\n",
    "\n",
    "<img src=\"figures/quantum_annealing_workflow.png\" alt=\"Software stack on a quantum annealer\" style=\"width: 400px;\"/>\n",
    "\n",
    "A possible classical solver for the Ising model is the simulated annealer that we have seen before:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-11-19T20:07:55.958097Z",
     "start_time": "2018-11-19T20:07:55.836641Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Energy of samples:\n",
      "[-2.0, -2.0, -2.0, -2.0, -2.0, -2.0, -2.0, -2.0, -2.0, -2.0]\n"
     ]
    }
   ],
   "source": [
    "import dimod\n",
    "\n",
    "J = {(0, 1): 1.0, (1, 2): -1.0}\n",
    "h = {0:0, 1:0, 2:0}\n",
    "model = dimod.BinaryQuadraticModel(h, J, 0.0, dimod.SPIN)\n",
    "sampler = dimod.SimulatedAnnealingSampler()\n",
    "response = sampler.sample(model, num_reads=10)\n",
    "print(\"Energy of samples:\")\n",
    "print([solution.energy for solution in response.data()])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's take a look at the minor embedding problem. This part is NP-hard in itself, so we normally use  probabilistic heuristics to find an embedding. For instance, for many generations of the quantum annealer that D-Wave Systems produces has unit cells containing a $K_{4,4}$ bipartite fully-connected graph, with two remote connections from each qubit going to qubits in neighbouring unit cells. A unit cell with its local and remote connections indicated is depicted following figure:\n",
    "\n",
    "<img src=\"figures/unit_cell.png\" alt=\"Unit cell in Chimera graph\" style=\"width: 80px;\"/>\n",
    "\n",
    "This is called the Chimera graph. The current largest hardware has 2048 qubits, consisting of $16\\times 16$ unit cells of 8 qubits each. The Chimera graph is available as a `networkx` graph in the package `dwave_networkx`. We draw a smaller version, consisting of $2\\times 2$ unit cells."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-11-19T20:07:56.523511Z",
     "start_time": "2018-11-19T20:07:55.961519Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/pwittek/.anaconda3/envs/qiskit/lib/python3.7/site-packages/networkx/drawing/nx_pylab.py:611: MatplotlibDeprecationWarning: isinstance(..., numbers.Number)\n",
      "  if cb.is_numlike(alpha):\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import dwave_networkx as dnx\n",
    "%matplotlib inline\n",
    "\n",
    "connectivity_structure = dnx.chimera_graph(2, 2)\n",
    "dnx.draw_chimera(connectivity_structure)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's create a graph that certainly does not fit this connectivity structure. For instance, the complete graph $K_n$ on nine nodes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-11-19T20:07:56.630653Z",
     "start_time": "2018-11-19T20:07:56.526970Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import networkx as nx\n",
    "G = nx.complete_graph(9)\n",
    "plt.axis('off') \n",
    "nx.draw_networkx(G, with_labels=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-11-19T20:07:56.647316Z",
     "start_time": "2018-11-19T20:07:56.632976Z"
    }
   },
   "outputs": [],
   "source": [
    "import minorminer\n",
    "embedded_graph = minorminer.find_embedding(G.edges(), connectivity_structure.edges())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot this embedding:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-11-19T20:07:56.765040Z",
     "start_time": "2018-11-19T20:07:56.651559Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dnx.draw_chimera_embedding(connectivity_structure, embedded_graph)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Qubits that have the same colour corresponding to a logical node in the original problem defined by the $K_9$ graph. Qubits combined in such way form a chain. Even though our problem only has 9 variables (nodes), we used almost all 32 available on the toy Chimera graph. Let's find the maximum chain length:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-11-19T20:07:56.771824Z",
     "start_time": "2018-11-19T20:07:56.766841Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4\n"
     ]
    }
   ],
   "source": [
    "max_chain_length = 0\n",
    "for _, chain in embedded_graph.items():\n",
    "    if len(chain) > max_chain_length:\n",
    "        max_chain_length = len(chain)\n",
    "print(max_chain_length)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The chain on the hardware is implemented by having strong couplings between the elements in a chain -- in fact, twice as strong as what the user can set. Nevertheless, long chains can break, which means we receive inconsistent results. In general, we prefer shorter chains, so we do not waste physical qubits and we obtain more reliable results."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# References\n",
    "\n",
    "[1] M. Fingerhuth, T. Babej, P. Wittek. (2018). [Open source software in quantum computing](https://doi.org/10.1371/journal.pone.0208561). *PLOS ONE* 13(12):e0208561.  <a id='1'></a>"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
